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107

Apr 12, 2014
04/14

by
Nikolaĭ Makarov

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Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

Source: http://books.google.com/books?id=OM0GAAAAQAAJ&oe=UTF-8

452
452

May 8, 2008
05/08

by
Nikolaĭ Makarov

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Book digitized by Google and uploaded to the Internet Archive by user tpb.

Source: http://books.google.com/books?id=ktANAAAAIAAJ&oe=UTF-8

10
10.0

Sep 19, 2013
09/13

by
Nikolai Makarov; Stanislav Smirnov

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We suggest how versions of Schramm's SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain.

Source: http://arxiv.org/abs/0909.5377v1

7
7.0

Sep 21, 2013
09/13

by
Haakan Hedenmalm; Nikolai Makarov

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We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral droplet. We also study the evolution of incrementally adding a dimension, i.e., adding an extra electron in this fermionic model.

Source: http://arxiv.org/abs/1106.2971v3

21
21

Sep 23, 2013
09/13

by
Haakan Hedenmalm; Nikolai Makarov

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In this note, we discuss the quantum Hele-Shaw flow, a random measure process in the complex plane introduced by the physicists P.Wiegmann, A. Zabrodin, et al. This process arises in the theory of electronic droplets confined to a plane under a strong magnetic field, as well as in the theory of random normal matrices. We extend a result of Elbau and Felder to general external field potentials, and also show that if the potential is $C^2$-smooth, then the quantum Hele-Shaw flow converges, under...

Source: http://arxiv.org/abs/math/0411437v1

10
10.0

Sep 22, 2013
09/13

by
Nam-Gyu Kang; Nikolai Makarov

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In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie derivatives. Based on this approach, we explain some equations of conformal field theory and outline their relation to SLE theory.

Source: http://arxiv.org/abs/1101.1024v3

50
50

Jul 24, 2013
07/13

by
Yacin Ameur; Haakan Hedenmalm; Nikolai Makarov

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In this note, we prove Gaussian field convergence of fluctuations of eigenvalues of random normal matrices in the interior of a quantum droplet.

Source: http://arxiv.org/abs/0807.0375v4

14
14

Sep 23, 2013
09/13

by
Yacin Ameur; Håkan Hedenmalm; Nikolai Makarov

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Consider the random normal matrix ensemble associated with a potential on the plane which is sufficiently strong near infinity. It is known that, to a first approximation, the eigenvalues obey a certain equilibrium distribution, given by Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. On a finer scale, one can consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of fluctuations,...

Source: http://arxiv.org/abs/1109.5941v1

20
20

Jul 22, 2013
07/13

by
Yacin Ameur; Haakan Hedenmalm; Nikolai Makarov

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We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion) paper.

Source: http://arxiv.org/abs/0807.0369v4